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# Questions tagged [cv.complex-variables]

Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

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### Singular set of entire functions

Recently I've started studying the theory of singular values for entire functions so I'm far from being a specialist in this field. In the literature I came across the following results: In  Gross ...
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### Holomorphic functions to complex torus

Let $X$ be a complex algebraic variety and $T$ a complex torus (not necessarily algebraic). Assume that $X$ is a proper subset of its completion $\bar{X}$. Let $f:X \to T$ be a holomorphic map. Are ...
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Let $f$ be a holomorphic function on the unit ball $B_1(0) \subseteq \mathbb{C}^n$. Then given any pair of constants $\delta, \epsilon > 0$, does there exist a smooth function $g: B_1(0) \to \... 0answers 227 views ### How strange are Hölder domains? Let$D$be a Jordan domain. We assume that$D$is a H?lder domain. Namely, there exists a H?lder continuous Riemann map$f$such that$D=f(\mathbb{D})$, where$\mathbb{D}$is an open unit disk. It ... 0answers 94 views ### How to calculate the contour integration? I encountered some problems when I read the paper. The details are shown as follows. \begin{equation} pdf(I)=e^I \prod_{i=1}^n \left(-j a_i\right)\int \frac{dk}{2\pi}\frac{e^{jk\left(e^I-1\right)}}{\... 1answer 295 views ### Does the$\overline{\partial}$operator have closed image? Let$X$be a complex-analytic manifold, not necessarily compact. Does$\overline{\partial} : C^\infty(X) \rightarrow \Omega^{0,1}(X)$have closed image with respect to the Fréchet topology given by ... 1answer 60 views ### Disk with punctures and convex geodesical hull of the punctures isomorphic? Consider a unit disk with marked points$z_i$,$i=1, \dots , n$on its boundary. Let us call this surface$X$. As it is well known, the disk can be equipped with an hyperbolic metric and is then ... 0answers 42 views ### Looking for a simple proof of approximating almost periodic functions by generalised trigonometric polynomials with restricted Bohr spectrum Let$AP$be the space of almost periodic functions, defined to be the uniform closure in$C_b(\mathbb R,\mathbb C)$of the set of generalized trigonometric polynomials$Q(t):=\sum_{j=1}^n a_j e^{i\...

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